Alexander Kazachkov, Tetyana Ignatova, Andrey Zholobenko

An amazing “rotating ring” optical illusion was studied in the frames of the students’ educational computer-based
research work. Virtual images of differently shaped moving objects were simulated in QBasic 71, MS Visual C++
6.0 and Borland Pascal and compared with the real-time frames and disks observed spinning against the contrast
background. Space distribution of background screening time τ was defined by direct measurement in virtual
experiments. Its perfect agreement with the dependence predicted by the kinematical model of the effect has
proved the illusion to be caused by space non-linearity of the ring’s background screening.

Optical illusions, kinematics, computer simulation of moving objects, QBasic 71, Visual C++ 6.0, Borland Pascal
MS, virtual measurements


Computer based education opens new and really unlimited possibilities for creative learning. In Physics
and relative subjects rote memorization and mechanically doing standard experimental labs fails to train
a creatively educated person. Learning by inquiry (Trowbridge, Bybee and Powell, 2000; Kawakatsu,
2001) is aimed at development of students’ skills and abilities to solve non-trivial problems by directed
gathering of information, its critical analysis, building and testing models of the observed phenomena.
To stimulate students’ interest in this – often complicated – educational approach, it is crucial to find
intriguing objects and processes to be studied and explained. It is no less important for the successful
and instructive educational inquiry to use attractive and efficient research facilities, like personal
computers and modern software.

Visual illusions caused by motion of an object of observation seem to be a splendid topic of the
computer-based students’ inquiry. To observe the “third coin” illusion (Gardner, 1986) and the famous
Pulfrich stereo illusion (Pulfrich, 1922; Walker, 1978), the simplest demonstrational equipment is
needed, no preliminary training required. In the authors’ experience, no one is left untouched by those
amazing visual effects, or unwilling to comprehend their mechanism. A well-developed Web-site presents, in particular, computer animations based on Carl Pulfrich’s
hypothesis of the delayed perception of dimmer images. Recently, computer-animated explanations of a
strikingly interesting “rotating” Pulfrich effect (Nickalls, 1986) have been reported (Nickalls,
Kazachkov, Vasylevska and Kalinin, 2002), together with the explicit kinematical model of the “third
coin” illusion. Three-dimensional computer simulation of the latter model is put on-line at

The “rotating ring” illusion was noticed by one of the authors (Alexander Kazachkov) in his preparation
of the report on spinning tops at the GIREP International Conference “Physics in New Fields and
Modern Applications – Opportunity for Physics Education” (Lund, Sweden, August 2002). Spinning a
ring made of stiff black rubber (a vacuum chamber seal) on the paper-covered table he was surprised to
“see an axis of rotation” (!). A bright strip of about the ring’s thickness wide made the ring’s vertical

diameter visible from any angle of observation. Taking that particular ring (50 mm in diameter, 5-mm
thick, black surface) and a white background was a lucky chance since an effect is extremely sharp with
it even at slow rotation. Thereafter, an illusion was tested on other objects of the kind easily available:
key rings, coins with the holes in the center (Yens, Denmark Crones) and never failed to be observed.
Moreover, if the conditions of illumination provide for sharp shadows, an “axis” is clearly seen in the
shadowy image also.


Educational research of the “ring’s axis illusion” was performed in a truly computer-based fasion. It
seemed quite natural to computer-simulate a spinning ring and try to obtain an effect by varying the
parameters of moving image (diameter and thickness of a ring, its color and frequency of “rotation”,
direction of “lightening”, color of the background, etc.). Three-dimensional ring images (see Figure 1)
were simulated with the popular OpenGL API used. Console application with GLUT or GL Utility
Toolkit libraries was chosen, to provide for the single interface for work with windows independently
of the platform. So, the structure of an application remains unchanged for Windows, Linux and other
operational systems. To observe the most realistic effects, video cards with 16Mb RAM and a minimum
500 MHz processor with 128 Mb RAM are needed. It should be noticed separately that color and
intensity of an object and the background should be chosen carefully to get rid of the visual after-effects
strong with bright contrast images.

                     Figure 1. Rotating ring, three-dimensional computer simulation

Spinning virtual rings visualized an axis of “rotation” nearly as clearly as their real prototypes. The
question yet remained whether an illusion is of a purely physiological nature or caused by physical
conditions of an experiment.

So, our educational inquiry was focused on building and testing an adequate model to explain the
rotating ring illusion. The best way to start this research was to consider a simplified problem of two
rectangular non-transparent oscillators moving antiphasely along the straight line (Figure 2).








 Figure 2. Rectangular oscillators as seen from above; A…G – consecutive stages of antiphase motion


Screening of the field of observation is determined by the oscillators’ law of motion. Simulation of
moving rectangles in MS Visual C++ 6.0, Borland Pascal and QBasic 71 allowed to define the duration
of screening τ of any chosen point along the rectangles’ path (x- axis) by direct “virtual measurement”.
It appeared that even in the simplest case of the constant velocity of rectangles’ motion, a rather sharp
peculiarity appears on the τ(x) graph – see Figure 3. For an observer, this reduced screening of bright
background is manifested in a lighter strip of an area dimmed by moving dark rectangles.

                                        1 ,0
                             , a .u .

                                        0 ,5
                             τ / τ

                                        0 ,0
                                               -0 ,8   -0 ,4   0 ,0   0 ,4   0 ,8
                                                        x /A , a .u .

Figure 3. Screening time of the oscillators’ background; d - the width of moving rectangles, V = const,
        A – respectively, velocity and amplitute of antiphase motion along an x-axis, τ0 = d/V

Just the same peculiarity is virtually “measured” on the τ(x) dependence of screening time for the case
of harmonic antiphase oscillations. That is a scenario close enough to an original observation of the
rotating ring. Virtual rectangles simulate segments of a spinning ring cut off by two parallel horizontal

planes, while symmetry axis of antiphase oscillators corresponds to the ring’s axis of rotation. An axis
neighborhood is visualized due to its minor screening (Figure 4). Rectangles’ turning points yield the
longest screening which in real time experiment is manifested in observation of the dark ring boundary
circling the gray inside area (here inertia of human vision plays the role also).

                                           0 ,0 4

                          τ / T , a .u .
                                           0 ,0 3

                                           0 ,0 2

                                           0 ,0 1

                                                         - 0 ,8   - 0 ,4   0 ,0   0 ,4   0 ,8
                                                                       x /A , a .u .

Figure 4. Screening time of the harmonic antiphase oscillators’ background; T, A – respectively, period
                                    and amplitute of oscillations

Reduced screening of the neighborhood of the ring rotation axis (and corresponding area in the case of
two-dimensional simulation) must be due to overlapping of non-transparent ring segments (dark
rectangles for simulation) moving towards each other in the plane of view – see Figure 1. This
hypothesis is supported by calculations of τ values for given x coordinates: τ(x) dependence obtained in
the antiphase harmonic oscillators model coincides with the one presented in Figure 4. An exact solution
gives a non-monotonical function:

                                                       2       x + d /2          x − d / 2 
                                           τ ( x) =     ar cos          − ar cos           
                                                       ω          A                 A      
for off-axis area: -A ≤ x ≤ -d/2, d/2 ≤ x ≤ A, and

                                                       1       x + d /2          − x − d / 2 
                                            τ ( x) =    ar cos
                                                                          − ar cos
                                                                                  
                                                                  A                  A       
in the axis neighborhood: -d/2 < x < d/2.

Here A is amplitude of rectangles’ oscillations (the rotating ring radius); d is their width (thickness of
the ring). As clearly seen from the exact solution, the width of the visualized axis area must be close to
the ring thickness d. That is in the full agreement with the observations of both real-time rotating rings
and their virtual simulators.


When explained, the “ring’s axis” illusion was started to be used as a computer-based students’ research
problem and a lecture demonstration. To evaluate educational impact of the proposed activity we should
emphasize keen interest in these studies displayed by the involved high school (graduation level) and
university (first and second year) students. Another “motional” optical illusion proved to be highly
educationally motivating. Students found it exciting to be engaged in a thorough – and no less amusing
– scientific investigations. Programming of electronic simulators of differently moving objects,
performance of “virtual measurements” and real-time graphing has advanced their computer skills and
knowledge. Learning Physics was also enhanced. Development of kinematical models followed by
derivation of spatial screening τ(x) dependencies for different laws of motion x(t), calculations and final

analysis were also instructive. Demonstration and explanation of the “axis” illusion to the younger
students was lively and well accepted.


Authors are thankful to Dr. V.G. Piryatinska for useful advice.


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Nickalls, R.W.D., Kazachkov, A.R., Vasylevska, Yu.V. and Kalinin, V.V., (2002). Motional Visual
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for Developing Scientific Literacy. Prentice-Hall Inc., Upper Saddle River, NJ, USA.

Walker, J., (1978). The Amateur Scientist. Scientific American, 3, 142.

Associate Professor Dr. Alexander Kazachkov
Physical Depatment
Kharkov National University
4, Svobody Sqr.
61077, Ukraine
Email: kazachkov@ilt.kharkov.u,

Tetyana Ignatova
Institute for Low Temperature Physics and Engineering
47 Lenin Ave.
61103, Ukraine

Andrey Zholobenko
Institute for Low Temperature Physics and Engineering
47 Lenin Ave.
61103, Ukraine


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